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CompactLong
CompactPrecision
CompactFFT

●概要

　CompactLongによる演算クラス。共有メソッドなのでNew は不要。

●設定、数学定数

○初期化

• Shared Sub SetUpCompact()
   明示的に初期設定する場合に用いる。FFTテーブル、数学定数が準備される。用いなくても、必要に応じて自動的に初期化される。

○数学定数

　以下の定数がプロパティとして参照できる。4095桁まで正しい。

• Shared ReadOnly Property PI() As CompactLong       π
• Shared ReadOnly Property dPI() As CompactLong     2π
• Shared ReadOnly Property hPI() As CompactLong     π/2
• Shared ReadOnly Property qPI() As CompactLong     π/4
• Shared ReadOnly Property E() As CompactLong        e
• Shared ReadOnly Property Ln10() As CompactLong   Ln10

●演算メソッド

○丸め、関係演算

• Shared Function Round(ByRef A As CompactLong) As CompactLong
   400１桁目で四捨五入し、4000桁の値を返す。
  　
• Shared Function Comp(ByRef A As CompactLong, ByRef B As CompactLong) As CompactRelation
• Shared Function Comp(ByRef A As CompactLong, ByVal B As Long) As CompactRelation
• Shared Function CompAbs(ByRef A As CompactLong, ByRef B As CompactLong) As CompactRelation
   符号付または絶対値で比較する。以下の結果が返る。
  
  Public Enum CompactRelation
     LessThan
     Equal
     GraterThan
     NA　　　　　　　(比較不能)
  End Enum

○四則演算

• Shared Function Add(ByRef A As CompactLong, ByRef B As CompactLong) As CompactLong
• Shared Function Add(ByRef A As CompactLong, ByVal B As Long) As CompactLong
  　
• Shared Function Subt(ByRef A As CompactLong, ByRef B As CompactLong) As CompactLong
• Shared Function Subt(ByRef A As CompactLong, ByVal B As Long) As CompactLong
  　
• Shared Function Mul(ByRef A As CompactLong, ByRef B As CompactLong) As CompactLong
• Shared Function Mul(ByRef A As CompactLong, ByVal B As Long) As CompactLong
   自動的に最適な乗算方法で乗算。
  　
• Shared Function LMul(ByRef A As CompactLong, ByRef B As CompactLong) As CompactLong
• Shared Function LMul(ByRef A As CompactLong, ByVal B As Long) As CompactLong
   従来方法による乗算。
  　
• Shared Function FMul(ByRef A As CompactLong, ByRef B As CompactLong) As CompactLong
   FFT乗算。
  　
• Shared Function Div(ByRef A As CompactLong, ByRef B As CompactLong) As CompactLong
• Shared Function Div(ByRef A As CompactLong, ByVal B As Long) As CompactLong
   自動的に最適な方法で除算。
  　
• Shared Function LDiv(ByRef A As CompactLong, ByRef B As CompactLong) As CompactLong
• Shared Function LDiv(ByRef A As CompactLong, ByVal B As Long) As CompactLong
   従来方法による除算。
  　
• Shared Function RDiv(ByRef A As CompactLong, ByRef B As CompactLong) As CompactLong
   逆数法による除算。逆数は多段初期値法でニュートン漸化式で算出している。
  　
• Shared Function Modulo(ByRef A As CompactLong, ByRef B As CompactLong, ByRef Quitient As CompactLong) As CompactLong
   Quitient = A \ B (整数商) となり、A Mod B (剰余)を返す。
  　

●数学関数

　公称精度の4000桁までは保証する努力をしている。

○階乗

• Shared Function Factorial(ByVal A As Integer) As CompactLong
• Shared Function FactorialDouble(ByVal A As Integer) As CompactLong
   二重階乗 A!! を返す。

○逆数

• Shared Function ReciproBasic(ByRef A As CompactLong) As CompactLong
   単一初期値によるニュートン法で求めたもの。
  
  
• Shared Function Recipro(ByRef A As CompactLong) As CompactLong
   多段初期値によるニュートン法で求めたもの。

○平方根/立方根

• Shared Function Sqrt(ByRef A As CompactLong) As CompactLong
• Shared Function Cbrt(ByRef A As CompactLong) As CompactLong

○指数関数

• Shared Function Exp(ByRef A As CompactLong) As CompactLong
   e^Aを返す。Aは任意の実数。
  
  
• Shared Function IPower(ByRef A As CompactLong, ByRef B As CompactLong) As CompactLong
• Shared Function IPower(ByRef A As CompactLong, ByVal B As Long) As CompactLong
   整数冪乗 A^Bを返す。Aは任意の実数。Bは整数または整数部が採用される。
  
  
• Shared Function Power(ByRef A As CompactLong, ByRef B As CompactLong) As CompactLong
   実数冪乗 A^Bを返す。A、Bは任意の実数。

○対数関数

• Shared Function Ln(ByRef A As CompactLong) As CompactLong
   自然対数。A ＞ 0。
  
  
• Shared Function Log(ByRef A As CompactLong) As CompactLong
   常用対数。A ＞ 0。
  
  
• Shared Function Log(ByRef A As CompactLong, ByRef B As CompactLong) As CompactLong
   任意対数。log_AB を返す。A ＞ 1。B ＞ 0。

○角度変換

• Shared Function Radian(ByRef A As CompactLong) As CompactLong    度→ラジアン
• Shared Function Radian(ByVal A As Long) As CompactLong    度→ラジアン
  
• Shared Function Degree(ByRef A As CompactLong) As CompactLong    ラジアン→度

○三角関数

• Shared Function Sin(ByRef A As CompactLong) As CompactLong
• Shared Function Cos(ByRef A As CompactLong) As CompactLong
• Shared Function Tan(ByRef A As CompactLong) As CompactLong
   Aはラジアン。

○逆三角関数

• Shared Function ASin(ByRef A As CompactLong) As CompactLong
• Shared Function ACos(ByRef A As CompactLong) As CompactLong
• Shared Function ATan(ByRef A As CompactLong) As CompactLong

○双曲線関数

• Shared Function Sinh(ByRef A As CompactLong) As CompactLong
• Shared Function Cosh(ByRef A As CompactLong) As CompactLong
• Shared Function Tanh(ByRef A As CompactLong) As CompactLong

○逆双曲線関数

• Shared Function ASinh(ByRef A As CompactLong) As CompactLong
• Shared Function ACosh(ByRef A As CompactLong) As CompactLong
• Shared Function ATanh(ByRef A As CompactLong) As CompactLong

○数学定数生成

　数学原始定数を4096桁精度で生成する。一般には使用しなく、内部で使用される。

• Shared Sub CreateE()
• Shared Sub CreatePIMatin()
• Shared Sub CreateLn10()